Issue

TROLL model currently compute leaf lifespan with Reich’s allometry (Reich et al. 1991). But we have shown that Reich’s allometry is underestimating leaf lifespan for low LMA species. Moreover simulations estimated unrealistically low aboveground biomass for low LMA species. We assumed Reich’s allometry underestimation of leaf lifespan for low LMA species being the source of unrealistically low aboveground biomass inside TROLL simulations. We decided to find a better allometry with Wright et al. (2004) GLOPNET dataset.

We tested different models starting from complet model Mcomp: \[ {LL_s}_j \sim \mathcal{logN}(log({\mu_s}_j),\,\sigma)\,, ~~s=1,...,S_{=4}~, ~~j=1,...,n_s\]

\[{\mu_s}_j = {\beta_0}*e^{{\beta_1}_s*{LMA_s}_j^{{\beta_3}_s} - {\beta_2}_s*{Nmass_s}_j^{{\beta_4}_s}}\] \[{\beta_i}_s \sim \mathcal{N}({\beta_i},\,\sigma_i)\,^I\] \[(\beta_i, \sigma, \sigma_i) \sim \mathcal{\Gamma}(0.001,\,0.001)\,^{2I+1}\]

LL graph

Figure 1: Leaf mass per area (LMA), leaf nitrogen content (Nmass) and leaflifespan (LL). Leaf mass per area (LMA in \(g.m^{-2}\)), leaf nitrogen content (Nmass, in \(mg.g^-1\)) and leaf lifespan (LL in \(months\)) are taken in GLOPNET dataset from Wright et al. (2004).

Model

\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA + {\beta_2}_s*N,\sigma)\,\] Maximum likekihood of 11.0675641 and \(R^2\) of 4.011824110^{30}

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + LMA^{{\beta_3}_s} + N^{{\beta_4}_s},\sigma)\,\] Maximum likekihood of 8.7566631 and \(R^2\) of 1.612299710^{32}

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA^{{\beta_3}_s} + {\beta_2}_s*N^{{\beta_4}_s},\sigma)\,\] Maximum likekihood of 9.3754692 and \(R^2\) of 1.017729710^{31}

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA + N,\sigma)\,\] Maximum likekihood of 8.9827971 and \(R^2\) of 3.283734610^{24}

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + LMA^{{\beta_3}_s} + N^{{\beta_4}_s},\sigma)\,\] Maximum likekihood of 9.1974485 and \(R^2\) of 3.554504210^{27}

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA^{{\beta_3}_s} + N^{{\beta_4}_s},\sigma)\,\] Maximum likekihood of 9.257722 and \(R^2\) of 6.074544210^{27}

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA,\sigma)\,\] Maximum likekihood of 8.9051831 and \(R^2\) of 5.398465610^{22}

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + LMA^{{\beta_3}_s},\sigma)\,\] Maximum likekihood of 9.1917157 and \(R^2\) of 6.528413310^{24}

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA^{{\beta_3}_s},\sigma)\,\] Maximum likekihood of 8.931063 and \(R^2\) of 6.279900410^{29}

Convergence

Results

Figure 3: Model predictions.